Prediction of threefold fermions in a nearly ideal Dirac semimetal BaAgAs

Materials with triply degenerate nodal points in their low-energy electronic spectrum produce crystalline-symmetry-enforced threefold fermions, which conceptually lie between the twofold Weyl and fourfold Dirac fermions. Here, we show how a silver-based Dirac semimetal BaAgAs realizes threefold fermions through our first-principles calculations combined with a low-energy effective k·p model Hamiltonian analysis. BaAgAs is shown to harbor triply degenerate nodal points, which lie on its C3 rotation axis, and are protected by the C6v (C2 - C3v) point-group symmetry in the absence of spin-orbit coupling (SOC) effects. When the SOC is turned on, BaAgAs transitions into a nearly ideal Dirac semimetal state with a pair of Dirac nodes lying on the C3 rotation axis. We show that breaking inversion symmetry in the BaAgAs1-xPx alloy yields a clean and tunable threefold fermion semimetal. Systematic relaxation of other symmetries in BaAgAs generates a series of other topological phases. BaAgAs materials thus provide another platform for exploring tunable topological properties associated with a variety of different fermionic excitations.